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Self-­interacting random walks and statistical physics [MA5941]

Summer semester 2020

Prof. Pierre Tarrès, John von Neumann Gastprofessor

Homepage: at NYU Shanghai Pfeil

Lecturer: Prof. Pierre Tarrès

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(Recommended) requirements:

MA2409 probability theory, MA2404 Markov chains

Contents:

The aim of the course is to introduce to some generic techniques for the study of self-­interacting random walks, and to explain the links that appeared recently with statistical physics, in particular with the supersymmetric hyperbolic sigma model arising in random matrix theory, with a random Schrödinger operator and with the so‐called Dynkin isomorphism and Ray-­Knight local time approaches. More information can be found here.

Exam

The exam will be in oral form (30 minutes). Students demonstrate that they have gained deeper knowledge of definitions and main mathematical tools and results on self-interacting random walks, particularly linearly edge-reinforced random walk, vertex-reinforced jump process, and their link to statistical physics.